# Questions tagged [beam]

Questions about the theory and applications of structural elements designed to resist bending.

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### Maximum Deflection for simply supported beam under arbitrary triangular loading

I am trying to get the: maximum deflection location of maximum deflection deflection at any point For a beam under an arbitrary triangular load (i.e. a, b, c, and w can vary). I tried to solve this ...
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### My solution of this deflection of beam problem not matching with the book solution

Here is the problem and it's solution done in book - https://imgur.com/a/DRS7OvN Here is my solution - https://imgur.com/a/Yd9JGuC The book solution has 1/384wL^4 term but I am getting 1/128wL^4. ...
40 views

### How to convert multiple point loads to uniformly distributed load

So I am working on a project with variables on how many point loads may be applied over a single span. Both ends are fixed, this is a constant. For example, I may have a beam which is 6m in overall ...
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### Timoshenko Fixed Fixed Total Beam Deflection

I am trying to solve a problem where there is a fixed-fixed (clamped-clamped) beam with a point load in the middle (at L/2). The L/H is less then the 10 required for normal beam bending analysis and ...
1 vote
86 views

### How to find the location on the 2-support beam where the deflection will be biggest?

Consider the uniform indeterminate beam as shown above. This beam is to be subjected to a single, 80N point load (acting down ) somewhere along its length. What is the procedure (i.e steps and logic) ...
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### Does the inertia of a beam section include the material density?

Sorry but I'm a little rusty. When solving a beam of any type of section, must the density be included in the moment of inertia of the section? For example, if I see Navier's formula, I would say ...
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81 views

### Get Node Numbers to Variable

I am using Andys APDL. I want to create Beam Element by entering Node numbers. Nodes numbers selection is through option “by location“ Then I don’t know how use them in element creation command i.e. E,...
113 views

### deflection of mild steel hollow tube beam

I am trying to compute the deflection of a hollow tube of mild steel, and my computation seems to give radically different results than a couple of online calculators. Apparently one is in error. The ...
1 vote
130 views

### Horizontal "pinching" force of an arch with applied moment

I have some Shape Memory Alloy wire programmed to curl from a straight beam into a circle. The force this generates is approximated as a uniform distributed bending moment along the length of the wire....
1 vote
34 views

### Beam load - bending design value of southern GC yellow pine for treehouse beam span

I'm looking to build a treehouse and wanting to ensure the support beams can carry a sufficient load over an 11-ft span. Based on page 78 (aka 83) of https://awc.org/wp-content/uploads/2021/12/AWC-...
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### Why is this bridge thickest above the support pillars instead of the mid-span where the bending stress is highest?

Why is a bridge designed like this? The depth of the section at pillars is more than the depth at middle. If I model this as a simply supported beam having load at mid span then the bending moment ...
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### How to design the thickness and diameter of a cantilever beam in bending for both composites and metals?

The goal is to find the optimum values of the diameter and the thickness of the circular cross-section of a cantilevered beam in bending, with the lowest weight (cross-sectional area). The main ...
90 views

### Any way to approximate effect of two point loads with just one?

Imagine a 3D problem where the goal is to calculate the max. cantilever beam deflection. There are 4 equal point loads A, B,C,D separated equally from the beam's major axis. Is there a way to ...
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### Max bending moment estimate

Context: I study aerodynamics and want to design and build an RC wing to put the theory I learned into practice. The essence of the theory I learned is: Given some mass of wing building material, how ...
90 views

### Magnitude of shear stress on beam element

In a previous question, the existence of a horizontal shear stress in a cantilevered I-beam with one free end was resolved. Here I'd like to explore the magnitude of the shear stress. Consider an I-...
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### Direction of shear in beam cross section - how to understand the convention

In an I-beam, the shear flow is usually shown drawn as on the left, not as drawn on the right. I do not understand why. I do understand: The total horizontal shear force must be zero, consistent with ...
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### How can I understand shear flow in a beam cross section?

I am trying to understand shear flow and I am just not getting it. For example, one of the problems in Beer has an I-beam and there is both a horizontal and vertical force acting on it. So it has ...
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### Are there disadvantages to using a single multispan beam, vs separate simple beams, for materials that tolerate tension as well as compression?

Suppose the following beam situation within a mundane building (viewed from above). Assume vibration and torsion aren't issues. Suppose we have a choice to span a gap in 2 different ways: (Grey = ...
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### Does the corbel angle govern in this scenario? If not, how is load spreading allowed for, when a load is supported by a wall on a beam

The following outline is inspired by something I noticed today and couldn't figure out. It shows what I guess is a fairly common generic situation - an upper floor masonry partition wall supported by ...
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### Analysing a multispan determinate beam by separating it into spans

Say we have the following indeterminate beam: We can make it determinate by adding a pin at B, and then adding back the bending moment at B which was destroyed by the pin: My lecture handouts then ...
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### Composite Cantilever Beam Analysis

I'm trying to solve this composite cantilever beam for deflection analysis. How should I proceed? I'm not from mechanical background. The connection between the elements is strong enough that the ...
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### Simply supported beam with a truss

i am trying to find out the best way to approach a design task for a plane wing with a truss support. i am treating the wing as a simply supported beam but i have no idea how to incorporate the truss ...
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125 views

### Rigidity and bending moment

When a beam which is fixed at one end and free at the other, is acted upon by a load P, the beam bends and we get a bending moment at every cross section of the beam. This bending moment can be ...
261 views

### What's the best shape (solid of revolution) for a cantilever beam to carry a point load at the free end?

How should you change the diameter/radius (while keeping constant overall volume) of the cross-section along the length of a round cantilever beam so that you minimise deflection with concentrated ...
1 vote
146 views

### Maximum deflection in the beam

Consider a simply supported beam, acted upon by a concentrated load P as shown By applying the method of successive integration, i.e. by using the differential equation $$EI \frac{d^2v}{dx^2} = M$$ ...
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### Forces supporting a beam

I've been struggling with this engineering problem. The forces I've got are Frb=2.08kN, Fray=15.12kN, and Frax=3kN. Before i give in my calculations I need to do a check if they are correct or not ...
1 vote
114 views

### Why the vertical shear stress in the flange neglected?

Consider a thin walled I section beam. At some intermediate c/s the shear force is V. The shear stress direction in flanges and web will be as shown. The textbook says that, the vertical shear ...
117 views

### How exactly the beam is twisting?

Consider an I section beam shown below, which is unsymmetric about the x-y plane. I apply a load P, at the centroid of this section. The textbook I follow, says that the member will twist apart from ...
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### First moment of area about the neutral axis

Consider a homogeneous beam with a rectangular c/s, its neutral axis will be at equal distances from the top and bottom edges. The first moment of the entire area about the NA will be zero, since we ...
79 views

### Should the stiffness of this cantilever beam be different for these two conditions?

So, I was just doing some Finite Element Analysis (FEA) to figure out what would be the effect on the stiffness of a cantilever beam if another beam is attached to it on its free end. Below shows the ...
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### How are beams arranged in a continuous concrete beam structure?

I am posed with this problem, where I am tasked to design multiple structural beams supporting a concrete slab. As a disclaimer, this problem is merely an exercise instead of a homework or a test, and ...
313 views

### Why in a rectangular cross section beam the shear stresses are parallel to the height throughout the surface?

Consider a beam with a rectangular c/s subjected to some arbitrary loading. At any cross section the shear force is V. This shear force is the resultant of all the internal resistive forces which act ...
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### Are there any stresses on this plane in a beam?

Consider a cantilever beam with a point load at its free end. If we cut the beam through a plane as shown (in which the load lies), to divide the beam into two parts, and if we isolate individual ...
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### Direction of Shear Stress on the periphery of a circular section beam

The Question is from shear stresses in beams Consider a beam made of circular cross section, in which at any cross section the shear force is V. The textbook I'm following states that - When a beam ...
104 views

### How is the limit state EQU used in Eurocode?

Quote from here: Limit state EQU, dealing with static equilibrium, is defined as: Loss of static equilibrium of the structure... considered as a rigid body, where minor variations in the [actions or ...
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### Due to what reason are the beams getting elongated?

I was studying about shear stresses in beams, where one of the ways the textbook tried explaining intuitively the presence of shear stresses in beams was: Source : Mechanics of Materials, R.C. ...
1 vote
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### Proving the advantage of a composite beam

The textbook that I'm following for studying bending stresses in beams, states that - "Engineers purposely design beams in this manner (composite manner) in order to develop a more efficient ...
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### Determining the ratio of bending moments in parts of a composite beam

Consider a composite beam formed by sandwiching a wood beam between two steel plates, whose cross section is shown. Say the beam is loaded by some arbitrary loading, due to which at any cross section ...
1 vote
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### Beam of uniform strength

Generally, for a given loading condition, the bending moment in a beam varies throughout its length due to which the maximum normal/bending stress at every section is different. For a given allowable ...
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### Dimensions of the wooden post

This question is regarding the following problem from Bending stresses in beams Problem: My solution and hence the answer doesn't match with the answer in the textbook. My Solution: The planks A will ...
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### How is the wire in this problem in pure bending?

Problem: A beam is said to be in pure bending if the bending moment in it remains constant throughout the length. The problem asks to determine the bending moment in the wire. In the solution of the ...
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### Confusion about sign of beam's moment force

A positive bending moment bends a beam concave upward(or towards the positive y direction), whereas a negative bending moment bends a beam concave downward(or towards the negative y direction). (...
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### Moment equilibrium equation of beam

The above beam is loaded by a distributed load per unit length of the referential scale defined by the vector field q = q(x) and a distributed moment load vector per unit length m = m(x). As a ...
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129 views

### Derivation of beam deflection equation

I have encountered the above beam deflection equation for a beam subjected to a linearly increasing distributed load while I was solving bisection method (https://itprospt.com/qa/159961/q3-15-points-...
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240 views

### How does one conclude from this, that neutral axis passes through the centroid?

The book I'm following for Strength of materials states that, in a beam with symmetric cross section (about the plane of bending) and in pure bending, the moment of cross sectional area about the ...
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### Deflection of Cantilever Beam with Midpoint Spring, Integration and Superposition Methods

How can I get the deflection required below using 1) the Integration and 2) Superposition methods (two ways)? The beam $AB$ is supported by a spring $CD$, which is fixed at $C$ with constant $k$, and ...
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1 vote
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### A problem on beams

Problem - I have interpreted "by hinging them together at B" as following - Now if this is the case, then applying a load on the right beam will have no effect, in my understanding, on ...
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### Slope of the Bending moment diagram where a point force acts

Consider a beam that is arbitrarily loaded and at any distance x, we take an element in the beam between two sections, where a point force acts as shown. Let us assume the directions of shear force ...
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### Solving Timoshenko beam equation for cantilever beam

Update with solution Solution 1 Problem: Beam clamped at left side, free end on right side, point load pointing downwards. x is defined positive from the clamped end towards the free end. Create FBD ...
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